Abstract
This paper considers a single-machine scheduling with linear deterioration rate of processing speed and multiple rate-modifying activities simultaneously. A rate-modifying activity can change the processing rate of machine under consideration, which means after each rate-modifying activity the speed of the machine is fully recovered. The integration of these two concept is motivated by human operators and semi-automatic systems that experience performance degradation over time and require rate-modifying activities for recovery. The objective is to minimize the makespan. We need to decide the sequence of jobs and when to schedule the rate-modifying activities. An optimal schedule is proposed, which can solve the problem in O(nlogn) time where n is the number of jobs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eilon, S.: On a mechanistic approach to fatigue and rest periods. Int. J. Prod. Res. 3, 327–332 (1964)
Gentzler, G.L., Khalil, T.M., Sivazlian, B.B.: Quantitative models for optimal rest period scheduling. Omega-Int. J. Manag. Sci. 5, 215–220 (1977)
Bechtold, S.E., Janaro, R.E., Sumners, D.L.: Maximization of labor productivity through multi-rest break scheduling. Manag. Sci. 30, 1442–1458 (1984)
Lee, C.Y., Leon, V.J.: Machine scheduling with a rate-modifying activity. Eur. J. Oper. Res. 128, 119–128 (2001)
Lee, C.Y., Lin, C.S.: Single-machine scheduling with maintenance and repair rate-modifying activities. Eur. J. Oper. Res. 135, 493–513 (2001)
Lodree, E.J., Geiger, C.D.: A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration. Eur. J. Oper. Res. 201, 644–648 (2010)
Lodree, E.J., Geiger, C.D., Jiang, X.: Taxonomy for integration scheduling theory and human factors: Review and research opportunities. Int. J. Ind. Ergonom. 39, 39–51 (2009)
Browne, S., Yechiali, U.: Scheduling deteriorating job on a single processor. Oper. Res. 38, 495–498 (1990)
Mosheiov, G.: ∧-shaped policies of schedule deteriorating jobs. J. Oper. Res. Soc. 47, 1184–1191 (1996)
Alidaee, B., Womer, N.K.: Scheduling with time dependent processing times: Review and extensions. J. Oper. Res. Soc. 50, 711–720 (1999)
Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing times. Eur. J. Oper. Res. 152, 1–13 (2004)
Zhao, C.L., Tang, H.Y.: A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity. Comput. Oper. Res. 39, 1300–1303 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Yu, S. (2013). An Optimal Single-Machine Scheduling with Linear Deterioration Rate and Rate-Modifying Activities. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-03780-6_29
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03779-0
Online ISBN: 978-3-319-03780-6
eBook Packages: Computer ScienceComputer Science (R0)